Personal Data

Full name

Maria Carlota da Rocha Xavier Rebelo Gonçalves

Publishing name

Maria Carlota da Rocha Xavier Rebelo Gonçalves

Birthday

1968-02-13T00:00:00

Academic Degrees

DOUTORAMENTO(0)

Degree date

1996

Final grade

Muito Bom com Distinção e Louvor

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Não se aplica

Supervisor

-

Co-supervisor

-

Scientific area

Análise Matemática

MESTRADO(0)

Degree date

1993

Final grade

Muito Bom

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Não se aplica

Supervisor

-

Co-supervisor

-

Scientific area

Análise Matemática

LICENCIATURA(0)

Degree date

1989

Final grade

18 valores

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Não se aplica

Supervisor

-

Co-supervisor

-

Scientific area

Análise Matemática

AGREGAÇÃO(0)

Degree date

2013

Final grade

Aprovado

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Não se aplica

Supervisor

-

Co-supervisor

-

Scientific area

Análise Matemática

Profissional activity

Period Position Institution
Maio 2015 - Professora Associada com Agregação Faculdade de Ciências da Universidade de Lisboa
Abril 2013 - Maio 2015 Professora Auxiliar com Agregação Faculdade de Ciências da Universidade de Lisboa
1988-1989 Monitora Fac. Ciências de Lisboa- Dep. de Matemática
1989-1993 Assistente Estagiária Fac. Ciências de Lisboa-Dep. de Matemática
1993- 1996 Assistente Fac. Ciências de Lisboa-Dep. de Matemática
Novembro 1996 - Abril 2013 Professora Auxiliar Fac. Ciências de Lisboa-Dep. de Matemática

Area of scientific activity

Area of scientific activity

Ordinary Differential Equations
Applications to Celestial Mechanics and Biomathematics

Specialization domain

Qualitative theory of ordinary differential equations. Topological methods, fixed point theorems.<br>Bifurcation theory.<br>Biomathematics.

Current main scientific area

Multiplicity of solutions of boundary value problems for second order equations in R^n.
<br>Epidemiological models.
Population dynamics models.
Kepler problem with dissipation.

Other scientific activities

- Organizer of the international conference: "Autumn School on Nonlinear Analysis and Differential Equations", Lisboa Setembro-Outubro de 1998.<br>- Organizer of the international school: "Summer School on Mathematical Biology", Lisboa Julho de 2002.<br>- Organizer of : "Topics in Differential Equations, a cycle of conferences at CMAF", Lisboa 2005.
-Organizer of E=mc^3, a spring to summer event of three mini-courses on dynamics and differential equations.

Experience as scientific advisor

Advisor of the Pos-doc Francesca Dalbono who had a Pos-doc fellowship from FCT during 2005 which was renewed for 2006

Supervisor (in collaboration with Alessandro Margheri from CMAF) of Nuno Carinhas which had a research fellowship from CMAF during the year 2005-2006.

Supervisor (in collaboration with Gabriela Gomes from IGC) of Paula Rodrigues, Ph.D. student at the Faculty of Sciences of the University of Lisbon. Paula Rodrigues finished her Ph.D. in October 2009.

Supervisor of the thesis of Teresa Caissotti in the Master Program in Mathematics for high-school teachers, 2011.

Supervisor of the thesis of Alexandre Simões in the Master Program in Mathematics, Universidade de Lisboa, 2016.

Supervisor (in collaboration with L. Sanchez) of the Post-doc Maurizio Garrione (CMAF) 2014.

Participations in R&D projects

Participated in "Acção Integrada Luso-Espanhola" from 2001 to 2004. As coordinator in 2003-2004.

Participated in the project "Epidemiologia e evolução
de doenças transmissíveis: gripe A e malária" (POCTI/Mat/47510/2002) whose coordinator was
Gabriela Gomes from Instituto Gulbenkian da Ciência.

Principal investigator of the project POCI/MAT/57258/2004 (Equações Diferenciais e Aplicações à Epidemiologia).

Participated in "Acção Integrada Luso-Espanhola" 2010-2011.

Participated in the project "Nonlinear Dynamics of ordinary differential equations and applications" (PTDC/Mat/113383/2009) whose coordinator is Alessandro Margheri from Universidade de Lisboa.



Awards

Year Award Awarding entity
1997 Programa de Estímulo à Investigação, área dos métodos matemáticos para a Biologia Fundação Calouste Gulbenkian

Publications

Artigos em revistas de circulação internacional com arbitragem científica

Artigos em revistas de circulação internacional com arbitragem científica

  • [17] A. Margheri, C. Rebelo, F. Zanolin, Connected branches of initial points for asymptotic BVPs and applications to heteroclinic solutions, Advanced Nonlinear Studies 9 (2009), 95-135.

Artigos em revistas de circulação internacional com arbitragem científica

  • [18] F. Dalbono, C. Rebelo, Multiplicity of solutions of Dirichlet problems associated to second order equations in R^2, Proc. Royal Soc. Edinburgh, 52, (2009), 569-581.

    [19] P. Rodrigues, M. G. M. Gomes, A. Margheri, C. Rebelo, Heterogeneity in susceptibility to infection can explain high reinfection rates, Journal of Theoretical Biology, 259 (2009), 280-290.


Artigos em revistas de circulação internacional com arbitragem científica

  • [21] M. Gabriela M. Gomes, Ricardo Águas, João S. Lopes, Marta C. Nunes, Carlota Rebelo, Paula Rodrigues and Claudio J. Struchiner, How host
    heterogeneity governs tuberculosis reinfection?, Proc. R. Soc. B, 279, (2012) 2473-2478 doi: 10.1098/rspb.2011.2712

Artigos em revistas de circulação internacional com arbitragem científica

  • [22] C Rebelo, A Margheri and N. Bacaer, "Persistence in seasonally forced epidemiological models", J. Math. Biol. , 64, (2012) 933–949 DOI: 10.1007/s00285-011-0440-6.

    [23] A. Margheri, R. Ortega, C.Rebelo, Some analytical results about periodic orbits in the restricted three body problem with dissipation, Celest Mech Dyn Astr, 113, (2012) 279--290 doi: 10.1007/s10569-012-9415-1

Artigos em revistas de circulação internacional com arbitragem científica

  • [24] A. Margheri, C. Rebelo, F. Zanolin, Complex dynamics in pendulum-type equations with variable length, J Dyn Diff Equat 25, (2013) 627--652 doi: 10.1007/s10884-013-9295-4

    [25] M. G. M. Gomes, M. Lipsitch, A. R. Wargo, G. Kurath, C. Rebelo, G. F. Medley, A. Coutinho, A missing dimension in measures of vaccination impacts, Plos Pathogens, 10 (2014).

    [26] C. Rebelo, A. Margheri and N. Bacaer, Persistence in some periodic epidemic models with infection age or constant periods of infection, DCDS-B, 19, (2014) 1155-1170.

    [27] A. Margheri, C. Rebelo, and P. Torres, On the use of Morse index and rotation numbers for multiplicity results of resonant BVPs, JMAA, 413, (2014) 660-667.

    [28] A. Margheri, R. Ortega, C.Rebelo, Dynamics of Kepler problem with linear drag Celest Mech Dyn Astr
    120, (2014), 19-38. DOI 10.1007/s10569-014-9553-8

Artigos em revistas de circulação internacional com arbitragem científica

  • [29] A. Margheri, C.Rebelo, M.G.M. Gomes, On the correlation between variance in individual susceptibilities and infection prevalence in populations, Journal of Math. Biol., 71,(2015) 1643-1661. DOI 10.1007/s00285-015-0870-7, URL http://dx.doi.org/10.1007/s00285-015-0870-7.

    [30] A. Margheri, C.Rebelo, Multiplicity of solutions of asymptotically linear Dirichlet problems associated to second order equations in ${\bf R}^{2n+1}$, Topological methods in nonlinear analysis, 46,(2015) 1107-1118.

    [31] M. Garrione, C. Rebelo, Persistence in seasonally varying predator-prey systems via the
    basic reproduction number, Nonlinear Analysis: Real World Applications, 30, (2016) 73-98

    [32] M. G. M. Gomes, E. Gjini, J. Lopes, C. Souto-Maior and C. Rebelo,
    A theoretical framework to identify invariant thresholds in infectious disease epidemiology, Journal of Theoretical Biology, 395, (2016) 97- 102

    [33] A. Margheri, C. Rebelo and M.G.M. Gomes,
    Heterogeneity in disease risk induces falling vaccine protection with rising disease incidence, Dyn. Syst. 32, (2017), 148?163 DOI:10.1080/14689367.2016.1187115

    [34] A. Margheri, R. Ortega and C. Rebelo,
    First integrals for the Kepler problem with linear drag,
    Celestial Mechanics and Dynamical Astronomy, 127, (2017), 35-48 DOI: 10.1007/s10569-016-9715-y

Artigos em revistas de circulação internacional com arbitragem científica

  • [20] A. Margheri, C. Rebelo, F. Zanolin, Chaos in periodically perturbed planar Hamiltonian systems using linked twisted maps, Journal of Differential Equations, 249, (2010), 3233-3257.

Artigos em revistas de circulação internacional com arbitragem científica

  • [16] P. Rodrigues, M.G.M. Gomes, C. Rebelo, Drug-resistance tuberculosis - a reinfection model, Theoretical Population Biology, 71, (2007), 196-212.

Artigos em revistas de circulação internacional com arbitragem científica

  • [15] M.G. Gomes, A. Margheri, G. Medley, C. Rebelo, Dynamical behaviour of epidemiological models with suboptimal immunity and nonlinear incidence, Journal of Mathematical Biology, 51,(2005), 414-430.<br>

Livros (editor)

  • -Nonlinear analysis and its applications to differential<br> equations, Proceedings of the "Autumn School on Nonlinear Analysis<br> and Differential Equations", Lisbon 1998, PNLDE 43, Birkhauser 2001<br><br>- Proceedings of the "Summer School on Mathematical Biology", Lisbon 2002, Centro Internacional de Matemática 2002<br>

Publicações em actas de encontros científicos

  • C. Rebelo, F. Zanolin, Twist conditions and periodic solutions of<br>differential equations, Proceedings of Dynamic Systems and<br>Applications,(Atlanta 1995) 2, 469-476, Dynamic Publishers, Inc, 1996.<br><br>C. Rebelo, A glance at the periodic Ambrosetti-Prodi problem, Proceedings of Equadiff 1995, (Lisboa), L. Magalhães, C. Rocha e L. Sanchez Eds, pp 480-485, World Scientific 1998.<br>

Teses

  • C. Rebelo, Soluções<br>de uma equação diferencial ordinária com condições de fronteira<br>não lineares, dissertação de mestrado, Faculdade de Ciências da<br>Universidade de Lisboa, 1993.<br><br>C. Rebelo, Periodic<br>solutions of nonautonomous planar systems via the Poincaré- Birkhoff fixed<br>point theorem, dissertação de doutoramento, Faculdade de Ciências da Universidade de Lisboa, 1996.<br><br>

Artigos em revistas de circulação internacional com arbitragem científica

  • [1] M. Ramos, C. Rebelo, A Unified Approach to Min-max Critical Point<br>Theorems, Portugaliae Mathematica, 51, (1994), 489-516.<br><br>[2] C. Rebelo, L. Sanchez, Existence and multiplicity for an O.D.E. with<br>nonlinear boundary conditions, Differential Equations and Dynamical Systems,<br>3, (1995), 383-396.<br><br>[3] C. Rebelo, F. Zanolin, Multiplicity results for periodic solutions of <br>second order ODEs with asymmetric nonlinearities, Trans. Amer. Math. Soc., 348, (1996),<br>2349-2389.<br><br>[4] C. Rebelo, F. Zanolin, Multiple periodic solutions for<br> a second order equation with one-sided superlinear growth, Dynamics of<br>Continuous, Discrete and Impulsive Systems, 2, (1996), 1-27.<br><br>[5] C. Rebelo, A note on the Poincaré - Birkhoff fixed point theorem and<br>periodic solutions of planar systems, Nonlinear Analysis TMA, 29, (1997), 291-311.<br><br>[6] C. Rebelo, Multiple periodic solutions of second order equations with<br>asymmetric nonlinearities, Discrete and Continuous Dynamical<br>Systems, 3, (1997), 25-34.<br><br>[7] C. Rebelo, F. Zanolin, On the existence and multiplicity of branches of nodal <br>solutions for a class of parameter dependent Sturm-Liouville problems via the shooting <br>mapping, Differential and Integral Equations, 13, (2000),1473-1502.<br><br>[8] C. Rebelo, A note on uniqueness of Cauchy problems associated to planar Hamiltonian systems,<br>Portugaliae Mathematica, 57, (2000), 415-419.<br><br>[9] J. Mawhin, C. Rebelo, F. Zanolin, Continuation theorems for Ambrosetti-Prodi type periodic problems, <br>Communications in Contemporary Mathematics, 2, (2000), 87-126.<br><br>[10] M.C. Gomes, A. Margheri, C. Rebelo, Stability and persistence in a compartment model of <br>pulmonary tuberculosis, Nonlinear Analysis TMA, 48, (2002), 617-636.<br><br>[11] A. Margheri, C. Rebelo, F. Zanolin, Maslov-index, Poincaré-Birkhoff theorem and periodic <br>solutions of asymptotically linear planar Hamiltonian systems, J. of Differential Equations, 183, <br>(2002), 342-367.<br><br>[12] F. Dalbono, C. Rebelo, Poincaré-Birkhoff fixed point theorem and periodic solutions <br>of asymptotically linear planar Hamiltonian systems, Rend. Sem. Mat. Univ. Pol. Torino, 60, (2002), <br>Turin Lectures 233-263.<br><br>[13] A. Margheri, C. Rebelo, Some examples of persistence in epidemiological models, <br>Journal of Mathematical Biology, 46, (2003), 564-570.<br><br>[14] J. Campos, A. Margheri, R. Martins, C. Rebelo, A note on a modified version of the Poincaré-Birkhoff <br>theorem, Journal of Differential Equations, 203, (2004), 55-63.<br>

Communications

Comunicações orais por convite

-Multiplicity of solutions of Dirichlet problems associated to second order equations in R2, “The Sixth International Conference on Dynamical Systems and Differential Equations”, Universidade de Poitiers, França, Junho 2006.<br>

Comunicações orais por convite

<br>- Multiplicity of solutions of Dirichlet problems associated to second order equations in R2, “International Conference on Interdisciplinary Mathematical and Statistical Techniques", Instituto Politécnico de Tomar, Portugal, Setembro 2006.<br>

Comunicações orais por convite

- AMS - EMS - SPM International Meeting 2015 (Porto, 10 - 13 de Junho de 2015) (Título: Persistence in seasonally forced epidemiological models)

- An Afternoon of Nonlinear Problems (Milão, 27 Janeiro 2016) (Título: Multiplicity of solutions of BVPs associated to asymptotically linear equations)

- The first Joint Meeting Brazil- Italy in Mathematics (IMPA, Rio de Janeiro, Agosto-Setembro 2016)(Título: Persistence in seasonally varying predator-prey systems.)

- The Portuguese Meeting in Biomathematics (University of Beira Interior, October, 2016) Plenary speaker, (Título: Recent Results on Epidemiological Models and on Prey-Predator Models)

- Nonlinear Meeting in Udine 2017 (Università di Udine, January 2017) Plenary speaker, (Título: Recent results on epidemiological models and on prey-predator models)

Comunicações orais por convite

- Some results on epidemiological models, Qualitative Theory of Nonlinear Differential Equations 2013 (Trieste, Janeiro-Fevereiro de 2013).

- Second workshop on heterogeneity in host-pathogens systems (Instituto Gulbenkian da Ciência, Oeiras, Abril de 2013).

- Some results about epidemiological models, Equadiff 13 (Praga, Agosto de 2013).

- Multiplicity of Solutions of BVP Associated to Asymptotically Linear Second Order Equations, 10th AIMS Conference (Madrid, 7-11 Julho 2014)

Comunicações orais por convite

-Persistência em sistemas epidemiológicos com efeitos de sazonalidade, Dia das equações, Universidade de Braga, 10 de Setembro de 2010.

Comunicações orais por convite

-Persistence in Seasonally Forced Epidemiological Systems, AIMS 8th International Conference in Dresden, Germany, 25-28 de Maio de 2010.

Comunicações orais por convite

- The Poincaré-Birkhoff fixed point theorem, Università di Torino, November 2004

Comunicações orais por convite

-Gewhnliche Differentialgleichungen: Harmonic,<br>Subharmonic, Homoclinic, and Heteroclinic Solutions, (Oberwolfach Março 1999)<br><br>-Oscillations and catastrophes in the epidemiology of infectious diseases, FIIP, Coimbra, 12-14 Julho 2004<br><br>- Estabilidade e persistência num modelo para a tuberculose, Departamento de Matemática Aplicada da Universidade do Porto, 31 de Março de 2001.<br><br>- Teorema de Poincaré-Birkhoff e soluções periódicas de sistemas de sistemas hamiltonianos planos, Universidade do Porto, 10 de Dezembro de 2003.<br><br>- O teorema de Poincaré-Birkhoff e soluções periódicas de sistemas de sistemas hamiltonianos planos, IST, 19 de Dezembro de 2003.<br><br><br><br>Mini-course: "Poincaré-Birkhoff fixed point theorem and periodic solutions <br>of asymptotically linear planar Hamiltonian systems", Turin Fortnight Universidade <br>de Torino, 24-28 de Outubro de 2001<br><br>

Outras comunicações orais


Communications in international congresses:
- International Meeting on Ordinary Differential Equations and their
Applications (Florença, Setembro de 1993)

-Equazioni differenziali ordinarie e applicazioni, (Bressanone, Maio de 1995)

-Equadiff 1995, (Lisboa, Julho de 1995)

Outras:
- Análise Matemática de Modelos em Ciências Biológicas, Fundação Calouste Gulbenkian, Fevereiro de 2001.